Download - Modeling the Behavior of the S&P 500 Index
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Modeling the Behavior of the S&P 500 Index
Mary MalliarisLoyola University Chicago
10th IEEE Conference on Artificial Intelligence for Applications
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Structure of the S&P
• Random or Chaotic?• If a neural network can determine market
prices better than the random walk model, it would challenge the efficient market hypotheses and support a chaotic dynamics structure for the market
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Random Walk Model
P(t+1) = P(t) + e(t+1)Where e(t+1) is from a distribution with mean
mu and variance sigma-squared
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Chaotic Dynamics
• A chaotic function must satisfy three requirements:– It must sample infinitely many values– It is sensitive to initial conditions– The periodic points of the function are dense in R
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Backpropagation Neural Network
• Input layer• Hidden layer• Output layer• Each node applies a function to the sum of
weighted inputs and computes one output
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Data• Weekly data from each Friday for two years• 1989 and 1990• 10 variables:– S&P 500 closing Index– 3 month treasury bill interest rate– 30 year T. Bond interest rate– Weekly New York Stock Exchange volumn– M1, M2– Price/earnings ratio– Gold price, Crude Oil price– CBOE put/call ratio
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Network Structure
• One input layer• Two hidden layers – 24 nodes in the first hidden layer– 8 nodes in the second hidden layer
• One output
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Comparison
• 10 periods• MAD• MSE• Correlation between expected and actual
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Results
• Neural network outperformed the random walk model in each period
• This is supportive of the deterministic structure of the stock market returns
• This is encouraging to researchers who wish to develop deterministic theories that may eventually replace the existing probabilistic paradigm.